Simple RNN时间序列预测

本文将介绍利用朴素的RNN模型进行时间序列预测

比方说现在我们有如下图所示的一段正弦曲线，输入红色部分，通过训练输出下一段的值

首先分析一下，假设我们一次输入50个点，batch设为1，每个点就一个值，所以input的shape就是[50, 1, 1]，这里我们换一种表示形式，把batch放在前面，那么shape就是[1, 50, 1]，可以这么理解这个shape，1条曲线，一共有50个点，每个点都是1个实数

import numpy.random import randint
import numpy as np
import torch
from torch import nn, optim
from matplotlib import pyplot as plt

num_time_steps = 50
start = randint(3) # [0, 3)
time_steps = np.linspace(start, start + 10, num_time_steps) # 返回num_time_steps个点
data = np.sin(time_steps) # [50]
data = data.reshape(num_time_steps, -1) # [50, 1]
x = torch.tensor(data[:-1]).float().view(1, num_time_steps - 1, 1) # 0~48
y = torch.tensor(data[1:]).float().view(1, num_time_steps - 1, 1) # 1~49

start表示的含义从几何上来说就是图上红色左边框的对应的横坐标的值，因为我们要确定一个起点，从这个起点开始向后取50个点，如果每次这个起点都是相同的，就会被这个网络记住

x是50个数据点中的前49个，我们利用这49个点，每个点都向后预测一个单位的数据，得到$\hat y$，然后将$\hat y$与$y$进行对比

接下来是构建网络架构

class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.rnn = nn.RNN(
            input_size=input_size,
            hidden_size=hidden_size,
            num_layers=1,
            batch_first=True,
        )
        self.linear = nn.Linear(hidden_size, output_size)

    def forward(self, x, h0):
        out, h0 = self.rnn(x, h0)
        # [b, seq, h] => [seq, h]
        out = out.view(-1, hidden_size)
        out = self.linear(out) # [seq, h] => [seq, 1]
        out = out.unsqueeze(dim=0) # => [1, seq, 1]
        return out, h0

首先里面是一个simple RNN，其中有个参数batch_first，因为我们数据传入的格式是batch在前，所以要把这个参数设为True。RNN之后接了个Linear，将memory的size输出为output_size=1方便进行比较，因为我们就只需要一个值

然后我们定义网络Train的代码

model = Net()
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr)

h0 = torch.zeros(1, 1, hidden_size) # [b, 1, hidden_size]

for iter in range(6000):
    start = np.random.randint(3, size=1)[0]
    time_steps = np.linspace(start, start + 10, num_time_steps)
    data = np.sin(time_steps)
    data = data.reshape(num_time_steps, 1)
    x = torch.tensor(data[:-1]).float().view(1, num_time_steps - 1, 1)
    y = torch.tensor(data[1:]).float().view(1, num_time_steps - 1, 1)

    output, h0 = model(x, h0)
    h0 = h0.detach()

    loss = criterion(output, y)
    model.zero_grad()
    loss.backward()
    optimizer.step()

    if iter % 100 == 0:
        print("Iteration: {} loss {}".format(iter, loss.item()))

最后是Predict的部分

predictions = []
input = x[:, 0, :]
for _ in range(x.shape[1]):
    input = input.view(1, 1, 1)
    (pred, h0) = model(input, h0)
    input = pred
    predictions.append(pred.detach().numpy().ravel()[0])

假设x的shape是[b, seq, 1]，经过x[:, 0, :]之后就变成了[b, 1]，但其实前面说过了，batch值是1，所以input的shape就是[1, 1]，然后再展开成[1, 1, 1]是为了能匹配网络的输入维度

倒数第二行和第三行的代码做的事情是，首先带入第一个值，得到一个输出pred，然后把pred作为下一次的输入，又得到一个pred，如此循环往复，就把上一次的输出，作为下一次的输入

最后的输出图像如下所示

完整代码如下：

from numpy.random import randint
import numpy as np
import torch
import torch.nn as nn
import torch.optim as optim
from matplotlib import pyplot as plt

num_time_steps = 50
input_size = 1
hidden_size = 16
output_size = 1
lr=0.01

class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.rnn = nn.RNN(
            input_size=input_size,
            hidden_size=hidden_size,
            num_layers=1,
            batch_first=True,
        )
        self.linear = nn.Linear(hidden_size, output_size)

    def forward(self, x, h0):
        out, h0 = self.rnn(x, h0)
        # [b, seq, h]
        out = out.view(-1, hidden_size)
        out = self.linear(out)
        out = out.unsqueeze(dim=0)
        return out, h0

model = Net()
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr)

h0 = torch.zeros(1, 1, hidden_size)

for iter in range(6000):
    start = randint(3)
    time_steps = np.linspace(start, start + 10, num_time_steps)
    data = np.sin(time_steps)
    data = data.reshape(num_time_steps, 1)
    x = torch.tensor(data[:-1]).float().view(1, num_time_steps - 1, 1)
    y = torch.tensor(data[1:]).float().view(1, num_time_steps - 1, 1)

    output, h0 = model(x, h0)
    h0 = h0.detach()

    loss = criterion(output, y)
    model.zero_grad()
    loss.backward()
    optimizer.step()

    if iter % 100 == 0:
        print("Iteration: {} loss {}".format(iter, loss.item()))

start = randint(3)
time_steps = np.linspace(start, start + 10, num_time_steps)
data = np.sin(time_steps)
data = data.reshape(num_time_steps, 1)
x = torch.tensor(data[:-1]).float().view(1, num_time_steps - 1, 1)
y = torch.tensor(data[1:]).float().view(1, num_time_steps - 1, 1)

predictions = []
input = x[:, 0, :]
for _ in range(x.shape[1]):
    input = input.view(1, 1, 1)
    (pred, h0) = model(input, h0)
    input = pred
    predictions.append(pred.detach().numpy().ravel()[0])

x = x.data.numpy().ravel() # flatten操作
y = y.data.numpy()
plt.scatter(time_steps[:-1], x.ravel(), s=90)
plt.plot(time_steps[:-1], x.ravel())

plt.scatter(time_steps[1:], predictions)
plt.show()